Maths-
General
Easy
Question
What are the horizontal asymptotes for the graph
![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
Hint:
A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =
, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y = f(x)y = f x , where f(x)f x is a rational expression .
- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x = -3 and x = -4.
- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x - value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
x2 + 7x + 12 = 0
x2 + 3x + 4x + 12 = 0
x(x + 3) + 4(x + 3) = 0
(x + 3) (x + 4) = 0
x = -3 or x = -4
The vertical asymptote of the rational function is x =−3 and x = -4
This function has x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.
![](data:image/png;base64,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)
From the graph we can analyze that the vertical asymptote of the rational function is x = -3 and x = -4.
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How do you find vertical and horizontal asymptotes of a rational function?
What are the vertical asymptotes for the graph of ![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
How do you find vertical and horizontal asymptotes of a rational function?
What are the vertical asymptotes for the graph of ![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....
Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence.
an = 12 - 5n
Write an explicit formula for the arithmetic sequence.
an = 12 - 5n
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence.
an = 8 + 3n
Write an explicit formula for the arithmetic sequence.
an = 8 + 3n
Maths-General
Maths-
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction](data:image/png;base64,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)
Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x over denominator x minus 6 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence.
![a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Write an explicit formula for the arithmetic sequence.
![a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAARCAYAAACb3u1RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAkFJREFUeNrtWr9LAzEUDkVExMVBHDociIg4iJuIu0Nx6FocC+Lg7iAdxMXZTRykiAhSpENxK+LgUBAREfEfcChCBxEREc4X+oTzyLW5XH7e3YNvyJE2X768e3l5OUJy022rgAbgHfANeABsxPyPdYCfcR3nADXULzfDdgOoACawvQC4xWc8Rn/3nDs1OQVs5jqotSTieoBHzr5HgGq+mHy6FwB7gG5gW/QMEbWJiw6npvbFmbq0BcZzUU8purcAh4BJFOECUE442DDo4mK7U69gCjLIRjGaewPGO8fnZYvXVpvuFZxo0OqAkgHnsImLDqceA3QwCg+yA8D2kPFYTu2qnol1v8ZoET7QmNiibOKiOlrRyNkErA3pt8iI5L7jesqK9pH9PnFbCuZgH4ZIq+BiY6SeQYee5ejbYfTjHc+mtdWq+xvjQHJvyDlMcxGtf8ZZyHnAMWBckhPJ0tPF2m/k/F8xt/szOrGGIZKmuYjWP3n7T2OOO6JpZ4ijp4u130iu+6Rf/yxgrnUGuIro+0L6N1p3WB7akUzSFi6qnLqFkZo3OscZj3VQjKOnjEqOVWnfLkaQGr7ZXUbZhwrzg290EbAE6CkgagMXX+Ei8KQRspyaV0/XnFooj59iPFvGqBjMz9oaJpCEi2gu6uqNHXXskoCeaZi7kNGaZz3UPkkpFxcXlu5WTxrz9VQYvZXaCrWrKeXi4sIW8SBKcqfmt8vQ1tYk5m6mVHPJ8gdDmZp7j/wvD4XbaeBi8iLBycOXbfYLk7UPgKAaNAEAAAEZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPmE8L21pPjxtaT5uPC9taT48L21zdWI+PG1vPj08L21vPjxtc3ViPjxtaT5hPC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1Yj48bW8+KzwvbW8+PG1uPjIuNDwvbW4+PG1vPjs8L21vPjxtc3ViPjxtaT5hPC9taT48bW4+MTwvbW4+PC9tc3ViPjxtbz49PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21hdGg+1catWwAAAABJRU5ErkJggg==)
Maths-General
Maths-
Write an explicit formula for the arithmetic sequence. ![a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAAARCAYAAAC1m8zDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAnNJREFUeNrtWb9LQzEQfhQpDkUoUjo4CA6O4iYiIi5FRKQIDp1EBHF0cygdxH9AHAQRKSJSkCIOIi5SHAURBwdxcXIoQgeRUkpBL/QqISavafvy69EPviFp2nd3uZfcffW8PnRjHngDrAJrwDfgPnDYUX/GgTngs8+aIeAh8AF5hHN9GEIJuAKMUnOTwFtH/TkDbgJ/fNbcAZep8RLO9WEZvhy3X5SEq8ADzjw5/TPsZAS4CywD63i8jhpyyCZbdGAM+Op4bERJWASmBGVJkZ28xoyNo6MXwHSPRrWjCEHbYiuSwHWsCxeZzwoYo7TF+ySThBWm9Gghii/SHzLoDI1TTmB0wCZbVJ4aNLc5a3hJaHNsREnY8PlOnS2Wp5kF94aOeZtsUX2CxDHJSMc453hsuknCGj2o4tFO1x3fhjZJhS22I4aJ2A427ZNsEpYF1/Egex1/MgtmgE+GNsS0LTK6lwrUAo6Nbj/8GpMFznyKbUw+MDNbyPE6F00wbYuM7hU0JrA5CTI2uv0QPYdoosec+Twr0ex5TRU7gvXFuddU9XkgUgIRGx+xsNwJ2BlbbFG1eaSGI9rZAPpIpIp34JpEY9JJbFT70clzSth8DeDVnMU4/EMWO68cdV+nORpVA9+yEa+p9FcUOGSDLao2bxZllhqyhC+STHcsGxudSShTQ5IG7AT9reKLFJP58QRnbgpPHbom0fH3Sy+2dFtw67yORShIyC8JB/wIFBnUpehxPqS2mN48crK/4BXmsh+Bgyj1W8x4I6S2mN48UmIkQ+BH4Lhkrocrz5xar9qWsGxe6JKwwkgE7DgMtnQr1tqYfE748Qv8TP3RNq2SKgAAAQ50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+YTwvbWk+PG1pPm48L21pPjwvbXN1Yj48bW8+PTwvbW8+PG1zdWI+PG1pPmE8L21pPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3ViPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM8L21uPjxtbz47PC9tbz48bXN1Yj48bWk+YTwvbWk+PG1uPjE8L21uPjwvbXN1Yj48bW8+PTwvbW8+PG1uPjEwPC9tbj48L21hdGg+awzmUwAAAABJRU5ErkJggg==)
Write an explicit formula for the arithmetic sequence. ![a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAAARCAYAAAC1m8zDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAnNJREFUeNrtWb9LQzEQfhQpDkUoUjo4CA6O4iYiIi5FRKQIDp1EBHF0cygdxH9AHAQRKSJSkCIOIi5SHAURBwdxcXIoQgeRUkpBL/QqISavafvy69EPviFp2nd3uZfcffW8PnRjHngDrAJrwDfgPnDYUX/GgTngs8+aIeAh8AF5hHN9GEIJuAKMUnOTwFtH/TkDbgJ/fNbcAZep8RLO9WEZvhy3X5SEq8ADzjw5/TPsZAS4CywD63i8jhpyyCZbdGAM+Op4bERJWASmBGVJkZ28xoyNo6MXwHSPRrWjCEHbYiuSwHWsCxeZzwoYo7TF+ySThBWm9Gghii/SHzLoDI1TTmB0wCZbVJ4aNLc5a3hJaHNsREnY8PlOnS2Wp5kF94aOeZtsUX2CxDHJSMc453hsuknCGj2o4tFO1x3fhjZJhS22I4aJ2A427ZNsEpYF1/Egex1/MgtmgE+GNsS0LTK6lwrUAo6Nbj/8GpMFznyKbUw+MDNbyPE6F00wbYuM7hU0JrA5CTI2uv0QPYdoosec+Twr0ex5TRU7gvXFuddU9XkgUgIRGx+xsNwJ2BlbbFG1eaSGI9rZAPpIpIp34JpEY9JJbFT70clzSth8DeDVnMU4/EMWO68cdV+nORpVA9+yEa+p9FcUOGSDLao2bxZllhqyhC+STHcsGxudSShTQ5IG7AT9reKLFJP58QRnbgpPHbom0fH3Sy+2dFtw67yORShIyC8JB/wIFBnUpehxPqS2mN48crK/4BXmsh+Bgyj1W8x4I6S2mN48UmIkQ+BH4Lhkrocrz5xar9qWsGxe6JKwwkgE7DgMtnQr1tqYfE748Qv8TP3RNq2SKgAAAQ50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+YTwvbWk+PG1pPm48L21pPjwvbXN1Yj48bW8+PTwvbW8+PG1zdWI+PG1pPmE8L21pPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3ViPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM8L21uPjxtbz47PC9tbz48bXN1Yj48bWk+YTwvbWk+PG1uPjE8L21uPjwvbXN1Yj48bW8+PTwvbW8+PG1uPjEwPC9tbj48L21hdGg+awzmUwAAAABJRU5ErkJggg==)
Maths-General